Asked by bill
Ed needs to take out a loan for $7,000 to purchase a car. His bank has offered him a loan at 10.0% interest, compounded monthly, for 36 months or 10.5% interest, compounded monthly, for 24 months. Ed’s goal is to save as much money as possible by the time he pays off the loan. Which of the following statements best describes what Ed should be thinking?
a.
Since the monthly payment for the 36 month loan is lower, this loan will save more.
b.
Since the monthly payment for the 24 month loan is lower, this loan will save more.
c.
Since the finance charge for the 36 month loan is lower, this loan will save more.
d.
Since the finance charge for the 24 month loan is lower, this loan will save more.
All Answers 1
Answered by
GPT-5 mini
AI
Answer: d.
Ed should compare the total finance charge (total amount paid − principal). Compute monthly payments and totals:
- 36 months at 10.0% (monthly r = 0.10/12 ≈ 0.008333): monthly payment ≈ $226.31, total paid ≈ $8,147.16, finance charge ≈ $1,147.16.
- 24 months at 10.5% (monthly r = 0.105/12 ≈ 0.00875): monthly payment ≈ $323.89, total paid ≈ $7,773.36, finance charge ≈ $773.36.
The 24-month loan has the lower finance charge, so it saves Ed more overall despite the higher monthly payment.
Ed should compare the total finance charge (total amount paid − principal). Compute monthly payments and totals:
- 36 months at 10.0% (monthly r = 0.10/12 ≈ 0.008333): monthly payment ≈ $226.31, total paid ≈ $8,147.16, finance charge ≈ $1,147.16.
- 24 months at 10.5% (monthly r = 0.105/12 ≈ 0.00875): monthly payment ≈ $323.89, total paid ≈ $7,773.36, finance charge ≈ $773.36.
The 24-month loan has the lower finance charge, so it saves Ed more overall despite the higher monthly payment.
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